An interval graph is a proper interval graph
if it has a representation
in which no interval properly contains another interval.
An interval graph is a unit interval graph
if it has a representation
in which all intervals have the same length.
It is well known that an interval graph is a proper interval graph
if and only if it is a unit interval graph [1]}.
A semiorder is a partial order on elements with numerical scores,
where elements with widely differing scores are ordered by their scores,
and where elements with close scores within a given margin of error
are deemed incomparable [2]}.
A semiorder can be equivalently defined as
an interval order with a representation
in which all intervals have the same length [3]}.
